Titration acid-base spreadsheet

For a titration with EDTA, you can follow the derivation through and find that the formation constant, Kf, should be replaced in Equation 12-11 by the conditional formation constant, K, which applies at the fixed pH of the titration. Figure 12-12 shows a spreadsheet in which Equation 12-11 is used to calculate the Ca2+ titration curve in Figure 12-11. As in acid-base titrations, your input in column B is pM and the output in column E is volume of titrant. To find the initial point, vary pM until V, is close to 0. 

Spreadsheet Summary In Chapter 7 of Applications of Microsoft Excel in Analytical Chemistry, the first and second derivatives of an acid/base titration curve are plotted in order to better determine the titration end point. A combination plot is produced that simultaneously displays the pH versus volume curve and the second-derivative curve. Finally, an alternative plotting method, known as a Gran plot, is explored for locating the end point by a linear regression procedure. 

The availability of a master equation for acid-base titrations, and of convenient non-linear least-squares curve-fitting methods such as incorporated in Excel s Solver, have made the determination of the unknown sample concentration(s) relatively easy a spreadsheet is all that is required for such an analysis. Of course, there is no guarantee that all component... 

Because of the close analogy between acid-base and redox behavior, it will come as no surprise that one can use redox titrations, and also simulate them on a spreadsheet. In fact, the expressions for redox progress curves are often even simpler than those for acid-base titrations, because they do not take the solvent into account. (Oxidation and reduction of the solvent are almost always kinetically controlled, and therefore do not fit the equilibrium description given here. In the examples given below, they need not be taken... 

We should note that the pH calculated from the relatively simple equations presented here break down near the equivalence point for weak acids and bases because the assumptions used in deriving them no longer apply. Even for strong acid-base titrations, we reach a point very near the equivalence point where the ionization of water becomes appreciable compared to the acid or excess base concentration, and the calculations are in error. You can satisfy yourself of these limitations by inserting in the spreadsheet examples titrant values that are, say, 99.99% or 99.999% and see where the calculated pH falls off the otherwise smooth titration curve. 

Calculating acid-base titration curves Strong acids, strong bases (Table 8.1), p. 266 Spreadsheet calculations, p. 269 Weak acids, weak bases (Table 8.2), p. 272 Spreadsheet calculations, p. 277 Indicators (key equations 8.4, 8.5), p. 270 Titration of Na2C03, p. 280 Titration of polyprotic acids (Table 8.3), p. 281 Titration of amino acids, p. 286... 

See Problem 21 for a spreadsheet calculation of the Ca-EDTA titration curve in Figure 9.3 at pH 10. As with calculated acid-base titration curves, the calculations here break down very near the equivalence point due to simplifying assumptions we have made. 

Figure 20-11. Spreadsheet for weak acid-strong base titration curve.

In this chapter we have applied the methods of chapter 4 to ionic equilibria other than those between acids and bases. Of course, complexation, extraction, solubility, precipitation, and redox equilibria may also involve acid-base equilibria, which is why we treated acid-base equilibria first. The examples given here illustrate that the combination of exact theory with the computational power of a spreadsheet allows us to solve many problems that occur in quantitative chemical analysis, and to analyze experimental data accordingly. Even quite complicated titrations, such as the multi-component precipitation titrations, the von Liebig titration, and redox titrations involving many species and complicated stoichiometries, can be handled with ease. 

The approach that we have worked out for the titration of a monoprotic weak acid with a strong base can be extended to reactions involving multiprotic acids or bases and mixtures of acids or bases. As the complexity of the titration increases, however, the necessary calculations become more time-consuming. Not surprisingly, a variety of algebraic and computer spreadsheet approaches have been described to aid in constructing titration curves. 

A more efficient experimental design provides concentrations and standard deviations in fewer than nine experiments. One of many efficient designs is shown in Figure 7-12. Instead of titrating each acid by itself, we titrate mixtures of the acids. For example, in row 5 of the spreadsheet, a mixture containing 2 mL A, 2 mL B, and 2 mL C required 23.29 mL of 0.120 4 M NaOH, which amounts to 2.804 mmol of OH. In row 6, the acid mixture contained 2 mL A, 3 mL B, and 1 mL C. Other permutations are titrated in rows 7 and 8. Then row 5 is repeated independently in row 9. Column E gives mmol of base for each run. 

Figure 11-11 Spreadsheet that uses Equation 11-9 to calculate the titration curve for 50 mL of the weak acid 0.02 M MES (pKa = 6.27) treated with 0.1 M NaOH. We provide pH as input in column B and the spreadsheet tells us what volume of base is required to generate that pH. 

O Effect of pKa in the titration of weak acid with strong base. Use Equation 11-9 with a spreadsheet such as the one shown in Figure 11-11 to compute and plot the family of curves at the left side of Figure 11-3. For a strong acid, choose a large A"a, such as Ka = 102 or pKa = -2. 

HI A tetraprotic system. Write an equation for the titration of tetrabasic base with strong acid (B + H+ —>— —>—> BHJj+ You can do this by inspection of Table 11-6 or you can derive it from the charge balance for the titration reaction. Use a spreadsheet to graph the titration of 50.0 mL of 0.020 0 M sodium pyrophosphate (Na4P207) with 0.100 M HC104. Pyrophosphate is the anion of pyrophosphoric acid. 

Figure 20-11 illustrates a portion of a spreadsheet for the calculation of the titration curve of 2.500 mmol of a weak acid (pXa = 5) with 0.1000 M strong base. The volume required to obtain a given pH value was calculated for pH values from 3 to 12 in increments of 0.20. The formula used to calculate V in cell C9 is... 

Spreadsheet Summary The titration curve for a difunctional base being titrated with a strong acid is developed in Chapter 8 of Applications of Microsoft Excel in Analytical Chemistry. In the example studied, ethylene-diamine is titrated with hydrochloric acid. A master equation approach is explored, and the spreadsheet is used to plot pH versus fraction titrated. 

Spreadsheet Summary The alpha values for EDTA are obtained and used to plot a distribution diagram in Chapter 9 of Applications of Microsoft Excel in Analytical Chemistry. The titration of the tetraprotic acid EDTA with base is also considered. 

We will hot constract a diprotic titration curve here, but if you want a good mental exercise, try it You just can t make the simplifying assumptions that we can usually use with monoprotic acids that are sufficiently weak or not too dilute. See your CD, Chapter 8, for auxiliary data for the spreadsheet calculation of the titration curve for 50.00 mL 0.1000 M H2C1O4 versus 0.1000 M NaOH. You can download that and enter the Kai and Kai values for other diprotic acids and see what their titration curves look like. Try, for example, maleic acid. For the calculations, we used the more exact equations mentioned above for the initial pH, the first buffet zone, and the first equivalence point. We did not use the quadratic equation for the second equivalence point since Cr04 is a quite weak base (Kbi = 3.12 X 10 ). See Ref. 8 for other examples of calculated titration curves. 

Parts (a) and (e) can be solved with only two template spreadsheets one for titrating weak acids with strong bases and the other for titrating weak bases with strong acids. For a weak monoprotic acid, use a value of pKaj > 20 for a weak monoacidic base (e.g.NHj) use pKaj < 0. 

An Excel spreadsheet can be constructed with appropriate formulas (to include the effects of dilution of the sample by titrant) to simulate the titration of weak and strong acids and bases (Figure 18.21). Some simulations use a master equation to calculate all points on the titration others use separate equations for different regions of the curve, for example before the equivalence point, at the equivalence point and after the equivalence point. The concentration of different species at a particular pH is calculated from [H (aq)l, and the volume of titrant required to produce that amount of each species is calculated. 

Problems 14-41 through 14-43. We will set up spreadsheets that will solve a quadratic equation to determine [HsO ] or [OH ], as needed. While approximate solutions are appropriate for many of the calculations, the approach taken represents a more general solution and is somewhat easier to incorporate in a spreadsheet. As an example consider the titration of a weak acid with a strong base. Here and Vi represent initial concentration and initial volume. 

---